That which passes nowadays for science, and is taught as such in the schools, is nothing but a mass of disconnected, uncertain, and often contradictory opinions. A principle of unity and certainty is entirely lacking. If anything permanent and irrefutable is to be accomplished in science, everything hitherto considered true must be thoroughly demolished and built up anew. For we come into the world as children and we form judgments of things, or repeat them after others, before we have come into the full possession of our intellectual powers; so that it is no wonder that we are filled with a multitude of prejudices, from which we can thoroughly escape only by considering everything doubtful which shows the least sign of uncertainty. Let us renounce, therefore, all our old views, in order later to accept better ones in their stead; or, perchance, to take the former up again after they shall have stood the test of rational criticism. The recognized precaution, never to put complete confidence in that which has once deceived us, holds of our relation to the senses as elsewhere. It is certain that they sometimes deceive us--perhaps they do so always. Again, we dream every day of things which nowhere exist, and there is no certain criterion by which to distinguish our dreams from our waking moments,--what guarantee have we, then, that we are not always dreaming? Therefore, our doubt must first of all be directed to the existence of sense-objects. Nay, even mathematics must be suspected in spite of the apparent certainty of its axioms and demonstrations, since controversy and error are found in it also.